Least Common Multiple (LCM) of 13 and 88
The least common multiple (LCM) of 13 and 88 is 1144.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 13 and 88?
First, calculate the GCD of 13 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 88 = 0 remainder 13 |
| 2 | 88 ÷ 13 = 6 remainder 10 |
| 3 | 13 ÷ 10 = 1 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 112 | 2800 |
| 57 and 37 | 2109 |
| 133 and 103 | 13699 |
| 113 and 109 | 12317 |
| 98 and 31 | 3038 |